Free Access
Issue
ESAIM: M2AN
Volume 47, Number 3, May-June 2013
Page(s) 903 - 932
DOI https://doi.org/10.1051/m2an/2012061
Published online 17 April 2013
  1. C. Agut and J. Diaz, Stability analysis of the interior penalty discontinuous Galerkin method for the wave equation. INRIA Res. Report (2010). [Google Scholar]
  2. M. Ainsworth, P. Monk and W. Muniz, Dispersive and dissipative properties of discontinuous Galerkin finite element methods for the second-order wave equation. J. Sci. Comput. 27 (2006). [Google Scholar]
  3. D.N. Arnold, An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19 (1982) 742–760. [CrossRef] [MathSciNet] [Google Scholar]
  4. D.N. Arnold, F. Brezzi, B. Cockburn and L.D. Marini, Unified analysis of disconitnuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39 (2002) 1749–1779. [CrossRef] [MathSciNet] [Google Scholar]
  5. C. Baldassari, Modélisation et simulation numérique pour la migration terrestre par équation d’ondes. Ph.D. Thesis (2009). [Google Scholar]
  6. G. Benitez Alvarez, A.F. Dourado Loula, E.G. Dutrado Carmo and A. Alves Rochinha, A discontinuous finite element formulation for Helmholtz equation. Comput. Methods. Appl. Mech. Engrg. 195 (2006) 4018–4035. [CrossRef] [MathSciNet] [Google Scholar]
  7. G. Cohen, Higher-Order Numerical Methods for Transient Wave Equations. Springer, Berlin (2001). [Google Scholar]
  8. S. Cohen, P. Joly, J.E. Roberts and N. Tordjman, Higher-order triangular finite elements with mass-lumping for the wave equation. SIAM J. Numer. Anal. 44 (2006) 2408–2431. [CrossRef] [MathSciNet] [Google Scholar]
  9. S. Cohen, P. Joly and N. Tordjman, Higher-order finite elements with mass-lumping for the 1d wave equation. Finite Elem. Anal. Des. 16 (1994) 329–336. [CrossRef] [Google Scholar]
  10. M.A. Dablain, The application of high order differencing for the scalar wave equation. Geophys. 51 (1986) 54–56. [CrossRef] [Google Scholar]
  11. J.D. De Basabe and M.K. Sen, Stability of the high-order finite elements for acoustic or elastic wave propagation with high-order time stepping. Geophys. J. Int. 181 (2010) 577–590. [CrossRef] [Google Scholar]
  12. Y. Epshteyn and B. Rivière, Estimation of penalty parameters for symmetric interior penalty galerkin methods. J. Comput. Appl. Math. 206 (2007) 843–872. [CrossRef] [MathSciNet] [Google Scholar]
  13. S. Fauqueux, Eléments finis mixtes spectraux et couches absorbantes parfaitement adaptées pour la propagation d’ondes élastiques en régime transitoire. Ph.D. Thesis (2003). [Google Scholar]
  14. J.-C. Gilbert and P. Joly, Higher order time stepping for second order hyperbolic problems and optimal CFL conditions. Comput. Methods Appl. Sci. 16 (2008) 67–93. [CrossRef] [Google Scholar]
  15. M.J. Grote, A. Schneebeli and D. Schötzau, Discontinuous Galerkin finite element method for the wave equation. SIAM J. Numer. Anal. 44 (2006) 2408–2431. [CrossRef] [MathSciNet] [Google Scholar]
  16. M.J. Grote and D. Schötzau, Convergence analysis of a fully discrete dicontinuous Galerkin method for the wave equation. Preprint No. 2008-04 (2008). [Google Scholar]
  17. D. Komatitsch and J. Tromp, Introduction to the spectral element method for three-dimensional seismic wave propagation. Geophys J. Int. 139 (1999) 806–822. [CrossRef] [Google Scholar]
  18. P. Lax and B. Wendroff, Systems of conservation laws. Commun. Pure Appl. Math. XIII (1960) 217–237. [CrossRef] [MathSciNet] [Google Scholar]
  19. G. Seriani and E. Priolo, Spectral element method for acoustic wave simulation in heterogeneous media. Finite Elem. Anal. Des. 16 (1994) 37–348. [CrossRef] [Google Scholar]
  20. K. Shahbazi, An explicit expression for the penalty parameter of the interior penalty method. J. Comput. Phys. 205 (2005) 401–407. [CrossRef] [Google Scholar]
  21. G.R. Shubin and J.B. Bell, A modified equation approach to constructing fourth-order methods for acoustic wave propagation. SIAM J. Sci. Statist. Comput. 8 (1987) 135–151. [CrossRef] [MathSciNet] [Google Scholar]
  22. T. Warburton and J.S. Hesthaven, On the constants in hp-finite element trace inverse inequalities. Comput. Methods Appl. Mech. Engrg. 192 (2003) 2765–2773. [CrossRef] [MathSciNet] [Google Scholar]

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